Rotunda (geometry)

Set of rotundas
Example: pentagonal rotunda
Faces	1 n-gon 1 2n-gon n pentagons 2n triangles
Edges	7n
Vertices	4n
Symmetry group	Cnv, [n], (*nn), order 2n
Rotation group	Cn, [n]+, (nn), order n
Properties	convex

In geometry, a rotunda is any member of a family of cyclic-symmetric polyhedra. They are similar to a cupola but, instead of alternating squares and triangles, they alternate pentagons and triangles around an axis. The pentagonal rotunda is a Johnson solid.

Other forms can be generated with dihedral symmetry and distorted equilateral pentagons.

Examples

Rotundas

3	4	5	6	7	8
File:Green triangular rotunda.svg triangular rotunda	File:Green square rotunda.svg square rotunda	File:Green pentagonal rotunda.svg pentagonal rotunda	File:Green hexagonal rotunda.svg hexagonal rotunda	File:Green heptagonal rotunda.svg heptagonal rotunda	File:Green octagonal rotunda.svg octagonal rotunda

Star-rotunda

Star-rotundas

5	7	9	11
File:Pentagrammic rotunda.svg Pentagrammic rotunda	File:Heptagrammic rotunda.svg Heptagrammic rotunda	File:Enneagrammic rotunda.svg Enneagrammic rotunda	File:Hendecagrammic rotunda.svg Hendecagrammic rotunda

See also

• Birotunda

References

• Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
• Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.